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Dynamic Stiffness formulation of an orthotropic Plate for free vibration analysis by Classical Plate Theory

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Vijay B. Roundal , Prathamesh S. Gorane , Vijaykumar Javanjal , Kuldeep A. Mahajan , Sachin R. kandharkar , Anil Shirgire
» doi: 10.48047/ecb/2023.12.si6.515


Aircraft structures generally modeled as assemblies of thin-walled structural elements, in particular, the top and bottom skins, torsion box, ribs and webs of the wing idealized as plates. Thus, the free vibration analysis of such structures plays an important role in aircraft design. The purpose of this research is to develop the dynamic stiffness method for an accurate and efficient, free vibration analysis of an orthotropic plates and plate assemblies. Free vibration analysis of orthotropic plate investigated with the help of dynamic stiffness method using classical plate theory. In this study, firstly, the fundamental equation of the classical plate theory (CPT) for orthotropic plate briefly summarized. Secondly, the dynamic stiffness matrix based on the CPT formulated. Subsequent to this development, the assembly procedure and imposition of boundary conditions by suppressing appropriate degrees of freedom (penalty method) explained in Section. This followed by section, which highlights the application of the Wittrick–Williams (WW) logic for computation of natural frequencies of thick plates with various boundary conditions. The rectangular plates have two opposite edges simply supported, while all possible combinations of free (F),simply supported(SS) and clamped (C) boundary conditions are applied to the other two edges. Hamilton’s principle used to derive the governing differential equations of motion and natural boundary conditions in free vibration. Experimental validation carried out using FFT Analyzer. Finally, the study closes with comparison of the results obtained by CPT, DSM and FFT analyzer with concluding remarks.

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